This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Algorithms will be implemented that will cope effectively with stiffness that may arise from the mechanisms [unreadable]reactions and membrane fluxes - that are specified by the user and, therefore, are not known in advance. Ultimately, the algorithms should be as "turn-key" as possible in order to relieve a biological user of making a decision about the time step of numerical integration. A PDE solver (solvers) with a stable performance in the presence of vastly different time scales will be developed that, which will automatically produce a solution within a given tolerance (set to achieve a reasonable for biological applications accuracy). One of the requirements specific for biological applications is that the solver should be sufficiently fast. We will pursue sequential algorithms based on the idea of operator splitting with an improved time discretization error.